Detailed Description
To make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, in one embodiment, the present invention provides a spatial encryption method based on a three-dimensional CAP constellation, including: the method comprises the following steps of taking a Logistic map model as a first chaotic model and generating a first-stage masking factor for carrying out XOR operation on pseudorandom input data; the super four-wing chaotic model is used as a second chaotic model for generating a second-level masking factor and a third-level masking factor which are used for respectively carrying out displacement transformation and space transformation on the three-dimensional CAP constellation; a three level masking factor is used for the cryptographic modulation of the three dimensional CAP constellation.
In the embodiment, the Logistic map model and the hyper-four-wing chaotic model are combined, firstly, the XOR operation is carried out on the pseudo-random input data, then, the displacement transformation and the space transformation of the three-dimensional constellation are realized, and the effect of communication safety can be effectively improved; the space encryption method based on the three-dimensional CAP constellation increases the encryption flexibility, and simultaneously has higher encryption performance and better error rate performance because the Euclidean distance is larger than that of a two-dimensional constellation.
In this embodiment, preferably, the expression of the logistic map model is as follows:
un+1=kun(1-un)……①
wherein k is a bifurcation parameter, and the value range of k is more than 0 and less than or equal to 4; initial value u0The value range of (1) is (0); u. ofnExpressing a value obtained after a formula (I) is iterated for n times; and generating a first-level masking factor l by using a formula I, wherein the specific rule is as follows:
l=floor(mod(u*1e16,2))……②;
wherein mod represents the complementation, floor represents the rounding of decimal, and u is the chaotic sequence generated by the formula (i).
In this embodiment, the value of k in formula (i) is preferably 3.95.
Fig. 2 is a bifurcation diagram of the logistic map chaotic model according to the present invention.
In this embodiment, preferably, the expression of the hyper-four-wing chaotic model is as follows:
wherein, the parameters x, y and z are system state variables; a. b, c, d, e, k, m and n are system parameters and are constant numbers; w is a system state feedback variable; t is the step length, and the value is an integer larger than zero;
the process of generating the second level masking factor includes: generating x, y, z and w four chaotic sequences through an ultra-four wing chaotic model, generating a second-level masking factor by using x, y and z, and using the second-level masking factor as displacement amplitude transformation of a three-dimensional CAP (CAP phase CAP) constellation point coordinate, wherein the x-axis constellation point coordinate is transformed to mask a factor S1; the y-axis constellation point coordinate transformation masking factor S2; z-axis constellation point coordinate transformation masking factor S3; the specific transformation rule is as follows:
wherein x, y and z are variables in the formula III, mod represents the remainder operation, and floor represents rounding down the decimal.
In this embodiment, preferably, the process of generating the third level masking factor includes: generating a w chaotic sequence through an ultra-four wing chaotic model, generating a third-level masking factor by using w, and using the third-level masking factor S4 as the space transformation of the three-dimensional CAP constellation point coordinates, wherein the specific rule is as follows:
S4=floor(mod(w,8))+1……⑤
w is a variable in the formula (c), mod represents a remainder operation, and floor represents rounding down on a decimal.
In the present embodiment, a, b, c, d, e, k, m,The values of n are respectively as follows: a is 8; b is-1; c is-40; d is 1; e is 2; k is-14; m is 1; n is-2; the initial values of the variables x, y, z, w are: x is the number of0=0.1;y0=0.1;z0=0.1;w0=0.1。
Fig. 3 is a phase diagram of the hyper-four-wing chaotic model according to the present invention.
In one application scenario, the process of encrypted modulation of the three-dimensional CAP constellation includes: generating a pseudo-random bit sequence p, and carrying out XOR operation on the generated pseudo-random bit sequence p and a first-stage masking factor L to obtain a bit sequence L:
L=xor(p,l)……⑥;
namely, the one-stage covering based on the XOR operation of the pseudorandom bit sequence is realized;
performing serial-parallel conversion, namely performing serial-parallel conversion on the bit sequence subjected to the exclusive-or operation, and converting the bit sequence into three paths of parallel bit sequences to obtain a bit data set with 3 columns;
constellation mapping, namely, taking each row in a three-row parallel bit data group as a group, mapping each row of bit data into symbol information of constellation points according to a Gray mapping rule, and obtaining a three-dimensional CAP constellation map after mapping;
performing displacement transformation, namely performing displacement transformation on the constellation points in the three-dimensional CAP constellation diagram respectively, wherein x-axis constellation point coordinate transformation S1, y-axis constellation point coordinate transformation S2 and z-axis constellation point coordinate transformation S3 are performed; wherein
Assume a certain constellation point D in the three-dimensional CAP constellation diagrami=(Di1,Di2,Di3) Constellation point Di=(Di1,Di2,Di3) Sequentially obtaining constellation point coordinates D after displacement transformationi'=(Di'1,Di'2,Di'3) Wherein:
namely, the two-stage covering based on the constellation displacement transformation is realized;
FIG. 4 is a constellation diagram of 8 constellation points of a three-dimensional CAP constellation according to the present invention after two-stage masking;
space transformation, namely respectively carrying out space transformation on constellation points in the three-dimensional CAP constellation diagram, and carrying out a third-level masking factor S4iThe real number in the middle of 1-8 represents eight regions of a three-dimensional space respectively, and each region is represented by a coordinate point: 1,1]、II=[-1,1,1]、III=[-1,-1,1]、IV=[1,-1,1]、V=[1,1,-1]、VI=[-1,1,-1]、VII=[-1,-1,-1]、VIII=[1,-1,-1];S4ix、S4iy、S4izRespectively is a coordinate point of the x axis, the y axis and the z axis of the space corresponding to the masking factor; performing spatial transformation according to a third level masking factor S4, and performing displacement transformation to obtain constellation points D'iAfter spatial transformation, the coordinates of the constellation points become D "i=(D”i1,D”i2,D”i3) Wherein:
FIG. 5 is a three-level masked constellation diagram of 8 constellation points of the three-dimensional CAP constellation according to the present invention;
after the constellation points are encrypted by the three-level masking factor, performing M times of upsampling on the output symbol information to obtain the upsampled symbol information;
performing shaping filtering on the up-sampled symbol information by using three filters which are orthogonal to each other pairwise;
and adding the three paths of parallel symbol information to obtain a complete encrypted modulation signal.
In this embodiment, preferably, the spatial encryption method further includes: after receiving an encrypted modulation signal passing through a channel, sequentially carrying out matched filtering, down sampling, three-level constellation decryption based on space transformation and two-level constellation decryption based on displacement transformation, obtaining original symbol information according to a minimum Euclidean distance judgment method, carrying out first-level bit decryption based on XOR operation, and recovering an original bit sequence.
FIG. 6 is a constellation diagram after being correctly decrypted by the third and second level masking factors according to the present invention.
In conclusion, the Logistic map model and the hyper-four-wing chaotic model are combined, firstly, the XOR operation is carried out on the pseudo-random input data, then the displacement transformation and the space transformation of the three-dimensional constellation are realized, and the effect of communication safety can be effectively improved; the space encryption method based on the three-dimensional CAP constellation increases the encryption flexibility, and simultaneously has higher encryption performance and better error rate performance because the Euclidean distance is larger than that of a two-dimensional constellation.
In the embodiments provided in the present application, it should be understood that the disclosed apparatus and method can be implemented in other ways. The apparatus embodiments described above are merely illustrative, and for example, the flowchart and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of apparatus, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems which perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.
In addition, the functional modules in the embodiments of the present invention may be integrated together to form an independent part, or each module may exist separately, or two or more modules may be integrated to form an independent part.
The functions, if implemented in the form of software functional modules and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
In light of the foregoing description of the preferred embodiment of the present invention, many modifications and variations will be apparent to those skilled in the art without departing from the spirit and scope of the invention. The technical scope of the present invention is not limited to the content of the specification, and must be determined according to the scope of the claims.